Extracting timing and strength of each of a plurality of signals comprising an overall blast, impulse or other energy burst

Abstract

A method for extracting data from an overall signal, generated by a plurality of impulses, by use of a computer using wavelet transform analysis of timing and strength of each of said plurality of impulses is disclosed. The method includes using a Discrete Wavelet Transform analysis or a Continuous Wavelet Transform analysis.

1 . A method, comprising extracting data from a signal, the signal being generated by a plurality of impulses, by use of a computer using wavelet transform analysis of the signal to determine timing and characteristics of each of said plurality of impulses. 
     
     
         2 . The method according to  claim 1 , wherein the wavelet transform analysis comprises a discrete wavelet transform analysis. 
     
     
         3 . The method according to  claim 1 , wherein the wavelet transform analysis comprises a continuous wavelet transform analysis. 
     
     
         4 . A method of analyzing a blast event using Continuous Wavelet Transform (CWT) comprising:
 (a) collecting a signal produced by a blast recorded and on a seismograph;   (b) inputting the data to the recording medium of a computer;   (c) reading the collected signal into a computer program on the computer;   (d) determining a start, end, and time step for the data;   (e) choosing a wavelet type;   (f) calculating coefficients;   (g) determining the initial scale to use in the analysis and choosing a start, and end, and a scale interval;   (h) calculating CWT coefficients as a function of time and scale for the entire blast event;   (i) plotting a modulus of the absolute value of the coefficients in time-scale space on a 3D scalogram;   (j) determining both if the scale parameters, the scale parameters representing the frequency range, is appropriate, and qualitative characteristics of the signal, such that low-scale peaks indicate impulsive signal characteristics related to detonations;   (k) continuing to step (l) if the scale parameters are appropriate, and, if not, revising and rerunning the CWT at step (g); and   (l) stopping the analysis if the scalogram(s) contains sufficient information for the desired analysis.   
     
     
         5 . The method according to  claim 4 , further comprising if, in step (l), the scalogram(s) do not contain sufficient information for the desired analysis, determining the appropriate sensitivity for calculating a Wavelet Transform Maximum Modulus. 
     
     
         6 . The method according to  claim 5 , wherein the Wavelet Transform Maximum Modulus is calculated on the basis of two criteria:
 (a) that at a given “b”, a change in the Continuous Wavelet Transform modulus with respect to “b” is zero and is therefore a flat spot; and   (b) that the slope on either side of the flat spot goes downward, defining the flat spot as a relative peak.   
     
     
         7 . The method according to  claim 6 , wherein each peak is plotted in time-scale space. 
     
     
         8 . The method according to  claim 7 , wherein a locus of flat spots forms a ridge, the method further comprising use a location of the ridges to assess firing times of the detonations, through determining the location of the ridges occur along a time axis. 
     
     
         9 . The method according to  claim 8 , further comprising qualitatively determining a strength of the vibration from the amplitude of the ridges. 
     
     
         10 . The method according to  claim 9 , wherein, if the Wavelet Transform Maximum Modulus contains sufficient information for the desired analysis, stop the analysis and, if the Wavelet Transform Maximum Modulus does not contain sufficient information, calculate a Holder Exponent, and a W max  at a constant a and associate the Holder exponent and the W max  with explosive performance. 
     
     
         11 . The method according to  claim 9 , wherein for each of the ridges, the method further comprises:
 calculating a slope of the ridge, the slope in log-log space of W vs. scale being called the Holder exponent; and   calculating a maximum value of W at low scale.   
     
     
         12 . The method according to  claim 11 , further comprising, using the slope of the ridge and the maximum value of W to assess the explosive performance for each of the impulses. 
     
     
         13 . The method according to  claim 4 , wherein the signal comprises a vibration signal. 
     
     
         14 . A method for extracting data from a signal, the signal being generated by a plurality of impulses, the method comprising:
 (a) collecting signal data, the signal data including vibration produced by the blast recorded on a seismograph;   (b) inputting the signal data to a recording medium of a computer;   (c) reading the collected signal from the recording medium into a computer program on the computer;   (d) determining a start time, an end time, and a time step for the data;   (e) choosing an appropriate type of wavelet;   (f) determining a number of coefficients for the chosen wavelet type; and   (g) selecting one of a Continuous Wavelet Transform analysis and a Discrete Wavelet Transform analysis to analyze the data.   
     
     
         15 . The method according to  claim 14 , further comprising if, in step (g), the Discrete Wavelet Transform analysis is selected, performing the following steps:
 (h) calculating the coefficients for the chosen wavelet type;   (i) decomposing the signal data into a plurality of splits that are determined by discrete scales in a process called multiresolution, wherein the desired number of splits is chosen, and then the multiresolution calculation performed on the original signal;   (j) plotting the lowest scale split is plotted to determine if the wavelet type, number of coefficients, and number of splits is appropriate, and, if so, smoothing a data set consisting of individual wavelet peaks with an appropriate filter to define the contribution of individual impulses; and   (k) plotting the smoothed data set by the computer and reviewing the plotted smoothed data set to assess impulsiveness and amplitude and use the impulsiveness and amplitude to assess detonation effectiveness and fragmentation.   
     
     
         16 . The method according to  claim 15 , further comprising selecting a different wavelet and repeating steps (h)-(k). 
     
     
         17 . The method according to  claim 15 , further comprising determining a different number of coefficients and repeating steps (h)-(k). 
     
     
         18 . The method according to  claim 15 , further comprising selecting different multiresolution variables and repeating steps (j)-(k). 
     
     
         19 . The method according to  claim 15 , further comprising, altering the smoothing of the data set and repeating step (k). 
     
     
         20 . The method according to  claim 14 , further comprising if, in step (g), the Continuous Wavelet Transform analysis is selected, performing the following steps:
 (h) determining the initial scale to use in the analysis and choosing a start, and end, and a scale interval;   (i) calculating CWT coefficients as a function of time and scale for the entire blast event;   (j) plotting a modulus of the absolute value of the coefficients in time-scale space on a 3D scalogram;   (k) determining both if the scale parameters, the scale parameters representing the frequency range, is appropriate, and qualitative characteristics of the signal, such that low-scale peaks indicate impulsive signal characteristics related to detonations;   (l) continuing to step (l) if the scale parameters are appropriate, and, if not, revising and rerunning the CWT at step (g); and   (m) stopping the analysis if the scalogram(s) contains sufficient information for the desired analysis.